The value of \(F_{x,y}\)  becomes zero when \(M_x\rightarrow M_y\) , and
it increases with
the mass splitting among the new scalars. Note that \(\Delta T\)  has little to do with \(D_{i}\)  since there is neither mixing between \(D_i\)  and the SM leptons nor tree-level mass splitting among \(D_{i}\) , while the deviation for the \(S\)  parameter can also be ignored [1]}. The formulae of Eq. (REF ) is a general result for the models with the mixings between the inert doublet and singlet scalars.
The global fitting results constrain \(\Delta T\)  at \(1.5-1.7\sigma \)  deviation by \(-0.02<\Delta T <0.12\)  [2]}.
We show \(\Delta T\)  as a function of \(M_{S_2}\)  in Fig. REF , where we have used \(M_{S_1}=310\,{\rm GeV}\)  and \(s_\theta =0.1(0)\)  along with (a) \(M_H=60\)  and (b) \(70\,{\rm GeV}\) . It is obvious that the numerical result of our model with \(s_\theta =0.1\)  is approximately equal to a pure inert doublet model with \(s_\theta =0\) . In general, \(\Delta T\)  goes up with increasing \(M_{S_2}\) , and for a large value of \(M_A-M_H\) , the constraint on \(M_{S_2}\)  becomes stronger. The figure also shows that \(M_A-M_H\)  is limited to be less than \(75\,{\rm GeV}\)  for \(M_H=60\)  to \(70\,{\rm GeV}\)  and \(90\lesssim M_{S_2}\lesssim 110\,{\rm GeV}\) . Finally, it should be noted that \(M_{S_2}\)  can not be too small, since there exists a lower bound on \(M_{S_2}\)  located within 70 to \(90\,{\rm GeV}\)  [3]} from the LEP experiments.
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